一类中立型退化时滞微分方程的周期解

讨论了一类中立型退化时滞微分方程的周期解的存在条件,并且给出了二维退化滞后微分方程的周期解的存在性问题,且给出了一个充要条件和两个充分条件,最后举例说明结论的有效性。     

中立型泛函微分方程的周期解

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。     

中立型泛函微分方程周期解问题

利用Fourier级数理论研究了一类k-阶线性中立型泛函微分方程周期解问题,给出了周期解存在唯一性的充要条件。利用此结果并结合Schauder不动点原理,进一步研究了一类k-阶非线性中立型泛函微分方程,得到了存在周期解的新的结果。这些结果改进和推广了近期文献中的已有结论。     

一类退化中立型微分系统的周期解

该文考虑一类退化中立型微分系统，利用不动点定理，得到了这类系统周期解存在的充分条件．     

一类非线性中立型微分方程周期解的存在性

利用有关不等式,本文首先获得一类非线性中立型微分方程一个新的先验估计.基于解的先验估计以及迭合度理论,给出了这类中立型微分方程存在周期解的一个充分条件.     

一类退化中立型微分系统的周期解

该文考虑一类退化中立型微分系统, 利用不动点定理, 得到了这类系统周期解存在的充分条件.     

高阶中立型微分方程的周期解

本文采用Ｆｏｕｒｉｅｒ级数理论,获得了任意阶常系数中立型微分方程周期解存在性和唯一性的充分必要条件     

一类高阶中立型泛函微分方程周期解

本文利用重合度理论讨论了一类高阶中立型泛函微分方程周期解的存在性,获得了若干结论.     

脉冲中立型微分方程的振动性

本文通过揭示脉冲中立型微分方程和与之相联系的中立型微分方程之间解的关系, 得出了脉冲中立型微分方程解振动的几个充分条件．     

高阶中立型微分方程的周期解

本文采用Fourier级数理论,获得了任意阶常系数中立型微分方程周期解存在性和唯一性的充分必要条件.     

Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward–backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman–Kac formula to the non-Markovian framework.     

POSITIVE PERIODIC SOLUTION TO SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH MIXED DELAY

We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii's fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.     

Equivariant Hopf bifurcation for neutral functional differential equations

In this paper we employ an equivariant Lyapunov-Schmidt procedure to give a clearer understanding of the one-to-one correspondence of the periodic solutions of a system of neutral functional differential equations with the zeros of the reduced bifurcation map, and then set up equivariant Hopf bifurcation theory. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction.

     

STUDY OF PERIODIC SOLUTIONS OF FOURTH ORDER NDE WITH DELAYS

Using Fourier series theory and techniques of real analysis inequality, some sufficient conditions of existence and uniqueness of periodic solutions for a class of fourth order neutral differential equations with some delays are obtained, the results extend and improve some known results.     

PERIODIC SOLUTIONS FOR A CLASS OF DEGENERATE NEUTRAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point method, discusses the problem of periodic solution for a class of degenerate neutral periodic system with delay, and obtains some sufficient conditions for the existence and uniqueness of periodic solution of the system, the result extends and improves some results of paper [1-2].     

一类脉冲中立型多种群时滞微分方程正周期解的存在性

利用新的重合度理论中的连续性定理,给出了一类带有脉冲的中立型时滞微分方程的正周期解的存在性判定定理.     

Triebel-Lizorkin空间上二阶有限时滞退化微分方程的适定性

本文在周期Triebel-Lizorkin空间F_(p,q)~s(T;X)上研究二阶有限时滞退化微分方程(Mu')'(t)+αu'(t)=Au(t)Gu'_t+Fu_t+f(t)(t∈T:=[0,2π]),u(0)=u(2π),(Mu')(0)=(Mu')(2π)的适定性.利用Triebel-Lizorkin空间上算子值傅里叶乘子定理,给出上述方程是F_(p,q~-)~s适定的充要条件.     

Differential algebraic equations with after-effect

In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.     

退化中立型微分系统的常数变易公式和通解

本文讨论退化中立型微分系统，将其分成三组系统，定义两种与其相应的基础解，并分别将其通解求出。从而给出退化中立型微分系统的通解以及常数变易公式，最终得出通解的明确表示，完全推广了常微分方程和时滞微分方程的基本理论。